I want to move vertices in an accurate way but the 3D Manipulator is missing
Looks like you set the 3d cursor as your pivot point.

I can't see the 3d Cursor is not to be see in your view. The 3d manipulator is in the same place as the 3d cursor, therefore is it offscreen as well.

Change the pivot point to any other setting (like median point) to the 3D Cursor show at the current selection.